The chance you'll go first in a duel is just that; chance. It's pure luck and we do not have items that increase that chance.
The chance you'll get something rare as a reward for a duel won, is just as much luck as going first. Each creature you encounter has a certain number of things in their pockets. Some items are at the top of the pocket and therefore fall out more easily when the creature is defeated. Some items are deep in those pockets and rarely fall out.